Depending what you are insulating it to do in there, laying stuff on top is the most practical, even if you don't want to.
At the low end, carpet pad and carpet (which, of course, does not work well for some uses, but does for others, and is far more insulated than a bare floor, while being easily reversed or removed for upgrade later.) Might only amount to R3, but when you're starting from R1, a total of R4 is a lot better than leaving it at R1.
An inch of foam and 1/4" of underlayment plywood could get you to R7 or R8 in in inch and a quarter of headroom lost with a smooth hard surface, if carpet won't suit the unspecified use.
"Access to a jack" (suitable for a small shed - no need for massive house jacks) is as simple as currently less money than a sheet of plywood costs, perhaps even less if you can focus your working time to fit a tool rental schedule. They are not unobtainable things that you either have, or never will have. They can be rented, or bought and then sold. Or you can very likely borrow the one in your vehicle.
The ply probably was laid on the platform before the walls went up. If you want to go through prying it up, you just cut it at or near the wall line to deal with that, and screw it back down when done. That may require some additional framing support where the walls are parallel to the joists, or you can deliberately leave enough extra wood when cutting to allow splicing it with a backer screwed to both sides of the cut line under the floor.